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A177923 a(1)=19, a(2)=13, a(3)=37; thereafter a(n) = gpf(a(n-1)+a(n-2)+a(n-3)), where gpf = "greatest prime factor". 3

%I

%S 19,13,37,23,73,19,23,23,13,59,19,13,13,5,31,7,43,3,53,11,67,131,19,

%T 31,181,11,223,83,317,89,163,569,821,1553,109,191,109,409,709,409,509,

%U 1627,509,23,127,659,809,29,499,191,719,1409,773,967,67,139,23,229,23,11,263,11,19,293,19,331,643,331,29,59,419,13,491,71,23,13,107,13,19,139,19,59,31,109,199,113,421,733,181,89,59,47,13,17,11,41,23,5,23,17,5,5,3,13,7,23,43,73,139,17,229,11,257,71,113,7,191,311,509,337

%N a(1)=19, a(2)=13, a(3)=37; thereafter a(n) = gpf(a(n-1)+a(n-2)+a(n-3)), where gpf = "greatest prime factor".

%C This is the periodic part of A177904 - it is periodic with period 212.

%C A smaller start is a(1)=3, a(2)=13, a(3)=7, but that would not produce the terms in the order of their first appearance in A177904.

%C There are several open questions concerning this class of sequences - see the Back-Caragiu reference in A177904.

%H N. J. A. Sloane, <a href="/A177923/b177923.txt">Table of n, a(n) for n = 1..212</a>

%t nxt[{a_,b_,c_}]:={b,c,FactorInteger[a+b+c][[-1,1]]}; NestList[nxt,{19,13,37},120][[All,1]] (* _Harvey P. Dale_, Dec 11 2018 *)

%Y Cf. A006530, A177904, A175723.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 18 2010

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Last modified January 28 05:02 EST 2022. Contains 350654 sequences. (Running on oeis4.)